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B. Baeumer, M. Kovcs and M. M. Meerschaer, “Numerical Solutions for Fractional Reaction-Diffusion Equations,” Computers and Mathematics with Applications, Vol. 55, No. 10, 2008, pp. 2212-2226. doi:10.1016/j.camwa.2007.11.012

has been cited by the following article:

• TITLE: Solving a Nonlinear Multi-Order Fractional Differential Equation Using Legendre Pseudo-Spectral Method

  AUTHORS: Yin Yang

  KEYWORDS: Legendre Pseudo-Spectral Method; Multi-Order Fractional Differential Equations; Caputo Derivative

  JOURNAL NAME: Applied Mathematics, Vol.4 No.1, January 28, 2013

  ABSTRACT: In this paper, we apply the Legendre spectral-collocation method to obtain approximate solutions of nonlinear multi-order fractional differential equations (M-FDEs). The fractional derivative is described in the Caputo sense. The study is conducted through illustrative example to demonstrate the validity and applicability of the presented method. The results reveal that the proposed method is very effective and simple. Moreover, only a small number of shifted Legendre polynomials are needed to obtain a satisfactory result.